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R. C. Cowsik ¹

Affiliations
1 Tata Institute of Fundamental Research, Bombay 400 005, IN

Abstract

Let A be a regular ring (for example, the polynominal ring in a finite number of indeterminates over a field). Let P be a prime ideal in A. In [1] Hochster raises the question whether it is possible to give conditions on A/P (for example, A/P Gorenstein) which imply that the powers of P are P-primary, (i.e. Pⁿ = P⁽ⁿ⁾ for all n).

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R. C. Cowsik ¹

Affiliations
1 Tata Institute of Fundamental Research, School of Mathematics, Colaba, Bombay 400 005, IN

Abstract

Hochster-Ratliff ([1] Proposition 4.10) have proved the same theorem without the projectivity condition. Here we prove that if A is Gorenstein at all maximal ideals containing M then A is Gorenstein.

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R. C. Cowsik ¹, M. V. Nori ¹

Affiliations
1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road Bombay 400 005, IN

Abstract

Let R be a Cohen-Macaulay ring and let M be its maximal ideal. Let 7 be a radical ideal of height r. Let X (= proj ΣIⁿ) -> Spec R be the "blow up" of the ideal I.

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